Focus diverse phase retrieval test results on broadband continuous wavefront sensing in space telescope applications

Continuous wavefront sensing benefits space observatories in on-orbit optical performance maintenance. To measure the phase of a wavefront, phase retrieval is an attractive technique as it uses multiple point spread function (PSF) images that are acquired by the telescope itself without extra metrology systems nor complicated calibration. The focus diverse phase retrieval utilizes PSFs from predetermined defocused positions to enhance the dynamic range of the algorithm. We describe an updated visible light active optics testbed with the addition of a linear motorized focus stage. The performance of the phase retrieval algorithm in broadband is tested under various cases. While broadband pass filters have advantages in higher signal-to-noise ratio (SNR), the performance of phase retrieval can be restricted due to blurred image caused by diffraction and increased computing cost. We used multiple bandpass filters (10 nm, 88 nm, and 150 nm) and investigated effects of bandwidth on the accuracy and required image acquisition conditions such as SNR, reaching accuracies below 20 nm RMS wavefront error at the widest bandwidth. We also investigated the dynamic range of the phase retrieval algorithm depending on the bandwidth and required amount of defocus to expand dynamic range. Finally, we simulated the continuous wavefront sensing and correction loop with a range of statistically generated representative telescope disturbance time series to test for edge cases.